An upright cylindrical tank is 10 feet in diameter and 10 feet high. If water in the tank is 6 feet deep. How much work is done in pumping all the water over the top edge of the tank?

I drew a picture in my notebook and tried to simplify the process, although I'm pretty sure as usual I'm doing most/all steps incorrectly.

The radius must be 5ft.

While this exercise doesn't list the weight of the water the whole chapter uses $\displaystyle \delta$ = 62.4 in pounds per cubic foot.

I'm reading examples which use cones instead of cylinders and literary guessing the following equations...

F = weight of water * distance

Weight of water = 62.4, distance = 6-y

F = $\displaystyle \delta\pi(6-y)$

W = F * D

I'm not sure if the integral should go from 0 to 10 or 0 to 6

$\displaystyle \delta\pi(6-y) * (6-y)dy$

I know this is a big mess, and I'm doing this horribly wrong but I just wanted to give my attempts before asking for help.

P.S I don't know what's wrong with these equations